Dynamo theory tells us that, to convert from 6 to 12v, the number of turns in both the field coil and armature needs to be doubled. Unfortunately there just isn't enough room in most dynamos to be able to achieve this. Yes, a thinner wire could be used but that creates another problem. The wire's current carrying capacity is directly proportional to its cross sectional area so halving the cross sectional area would also halve the current carrying capacity. Now, power in watts is equal to volts times amps. The standard 60 watt Lucas E3L dynamo is 60W because it was designed to produce 10 amps at 6 volts. If converted to 12v in the way just described, the thinner wire halves the current carrying capacity so we get 12 volts times 5 amps which works out to be the same 60 watts. Bearing in mind that the brightness of the lamps is measured in watts, you can see that there is no increase in power gained by converting to 12v in this way so the lights would be no brighter. That in itself is not a problem and certainly the lower amperage improves the efficiency of the wiring loom because there is less power loss in the loom with lower currents. Unfortunately, halving the cross sectional area of the wire still would not reduce the diameter enough to create enough room to double the number of turns. The wire would need to be reduced in diameter by a considerable amount which would reduce its current carrying capacity to an unacceptable level. In practice, this type of conversion could not be done – there simply is not enough room. Armatures and field coils ‘converted to 12v’ are a compromise on this theoretical ideal.
It is often the case that a poorly performing 6v system is the reason for choosing to change to 12v. When this is done, consider what the new system consists of. A newly overhauled dynamo ‘converted’ to 12v, a new 12v battery, a new 12v regulator, new 12v bulbs and so on. Chances are, while these parts are being changed, poor connections are noticed and corrected – maybe even a complete new wiring loom is fitted. In short, a new 12v system is bound to be so much better than the poor, worn out 6v system it replaces. A similar overhaul on the original 6v system is likely to produce very similar major improvements for a fraction of the cost.